Bond-Graph Modelling and Causal Analysis of Biomolecular Systems

  • Peter J. GawthropEmail author


Bond graph modelling of the biomolecular systems of living organisms is introduced. Molecular species are represented by non-linear C components and reactions by non-linear two-port R components. As living systems are neither at thermodynamic equilibrium nor closed, open and non-equilibrium systems are considered and illustrated using examples of biomolecular systems. Open systems are modelled using chemostats: chemical species with fixed concentration. In addition to their role in ensuring that models are energetically correct, bond graphs provide a powerful and natural way of representing and analysing causality. Causality is used in this chapter to examine the properties of the junction structures of biomolecular systems and how they relate to biomolecular concepts.


Bond Graph Junction Structure Stoichiometric Matrix Kernel Matrice Biomolecular System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Peter Gawthrop would like to thank the Melbourne School of Engineering for its support via a Professorial Fellowship. He would also like to thank Michael Pan and Joe Cursons for their close reading of the draft chapter.


  1. 1.
    Alberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K., et al. (Eds.). (2015). Molecular biology of the cell (6th ed.). Abingdon: Garland Science.Google Scholar
  2. 2.
    Alon, U. (2007). Introduction to systems biology: Design principles of biological networks. Boca Raton: CRC Press.Google Scholar
  3. 3.
    Atkins, P., & de Paula, J. (2011). Physical chemistry for the life sciences (2nd ed.). Oxford: Oxford University Press.Google Scholar
  4. 4.
    Beard, D. A. (2012). Biosimulation: Simulation of living systems. Cambridge: Cambridge University Press. ISBN: 978-0-521-76823-8.CrossRefGoogle Scholar
  5. 5.
    Beard, D. A., & Qian, H. (2010). Chemical biophysics: Quantitative analysis of cellular systems. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  6. 6.
    Breedveld, P. C. (1982). Thermodynamic bond graphs and the problem of thermal inertance. Journal of the Franklin Institute, 314(1), 15–40. ISSN: 0016-0032. doi: 10.1016/0016-0032(82)90050-3.
  7. 7.
    Cellier, F. E. (1991). Continuous system modelling. New York: Springer.CrossRefzbMATHGoogle Scholar
  8. 8.
    Cloutier, M., Bolger, F. B., Lowry J. P., & Wellstead P. (2009). An integrative dynamic model of brain energy metabolism using in vivo neurochemical measurements. Journal of Computational Neuroscience, 27(3), 391–414. ISSN: 0929-5313. doi: 10.1007/s10827-009-0152-8.
  9. 9.
    Fuchs, H. U. (1996). The dynamics of heat. New York: Springer.CrossRefzbMATHGoogle Scholar
  10. 10.
    Gawthrop, P. J., & Bevan, G. P. (2007). Bond-graph modeling: A tutorial introduction for control engineers. IEEE Control Systems Magazine, 27(2), 24–45. doi: 10.1109/MCS.2007.338279.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gawthrop, P. J., & Crampin, E. J. (2014). Energy-based analysis of biochemical cycles using bond graphs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 470(2171), 1–25. doi: 10.1098/rspa.2014.0459. Available at arXiv:1406.2447.
  12. 12.
    Gawthrop, P. J., & Crampin, E. J. (2016). Modular bond-graph modelling and analysis of biomolecular systems. IET Systems Biology, 10, 2016. ISSN: 1751-8849. doi: 10.1049/iet-syb.2015.0083. Available at arXiv:1511.06482.
  13. 13.
    Gawthrop, P. J., Cursons, J., & Crampin, E. J. (2015). Hierarchical bond graph modelling of biochemical networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2184), 1–23. ISSN: 1364-5021. doi: 10.1098/rspa.2015.0642. Available at arXiv:1503.01814.
  14. 14.
    Gawthrop, P. J., & Smith, L. (1992). Causal augmentation of bond graphs with algebraic loops. Journal of the Franklin Institute, 329(2), 291–303. doi: 10.1016/0016-0032(92)90035-F.CrossRefGoogle Scholar
  15. 15.
    Gawthrop, P. J., & Smith, L. P. S. (1996). Metamodelling: Bond graphs and dynamic systems. Hemel Hempstead: Prentice Hall. ISBN: 0-13-489824-9.Google Scholar
  16. 16.
    Greifeneder, J., & Cellier, F. E. (2012). Modeling chemical reactions using bond graphs. In Proceedings ICBGM12, 10th SCS International Conference on Bond Graph Modeling and Simulation, Genoa, Italy (pp. 110–121).Google Scholar
  17. 17.
    Hill, T. L. (1989). Free energy transduction and biochemical cycle kinetics. New York: Springer.CrossRefGoogle Scholar
  18. 18.
    Jamshidi, N., & Palsson, B. (2010). Mass action stoichiometric simulation models: Incorporating kinetics and regulation into stoichiometric models. Biophysical Journal, 98(2), 175–185. ISSN: 0006-3495. doi: 10.1016/j.bpj.2009.09.064.
  19. 19.
    Job, G., & Herrmann, F. (2006). Chemical potential – A quantity in search of recognition. European Journal of Physics, 27(2), 353–371 (2006). doi: 10.1088/0143-0807/27/2/018.
  20. 20.
    Karnopp, D. (1990). Bond graph models for electrochemical energy storage: Electrical, chemical and thermal effects. Journal of the Franklin Institute, 327(6), 983–992. ISSN: 0016-0032. doi: 10.1016/0016-0032(90)90073-R.
  21. 21.
    Karnopp, D. C., Margolis, D. L., & Rosenberg, R. C. (2012). System dynamics: Modeling, simulation, and control of mechatronic systems (5th ed.). New York: Wiley. ISBN: 978-0470889084.CrossRefGoogle Scholar
  22. 22.
    Klipp, E., Liebermeister, W., Wierling, C., Kowald, A., Lehrach, H., & Herwig, R. (2011). Systems biology. Weinheim: Wiley.Google Scholar
  23. 23.
    Lambeth, M. J., & Kushmerick, M. J. (2002). A computational model for glycogenolysis in skeletal muscle. Annals of Biomedical Engineering, 30(6), 808–827. ISSN: 0090-6964. doi: 10.1114/1.1492813.
  24. 24.
    Maxwell, J. C. (1871). Remarks on the mathematical classification of physical quantities. Proceedings London Mathematical Society, 3, 224–233.Google Scholar
  25. 25.
    Mukherjee, A., Karmaker, R., & Samantaray, A. K. (2006). Bond graph in modeling, simulation and fault identification. New Delhi: I.K. International.Google Scholar
  26. 26.
    Ort, J. R., & Martens, H. R. (1973). The properties of bond graph junction structure matrices. Journal of Dynamic Systems, Measurement, and Control, 95, 362–367. ISSN: 0022-0434. doi: 10.1115/1.3426736.
  27. 27.
    Oster, G., & Perelson, A. (1974). Chemical reaction networks. IEEE Transactions on Circuits and Systems, 21(6), 709–721. ISSN: 0098-4094. doi: 10.1109/TCS.1974.1083946.
  28. 28.
    Oster, G., Perelson, A., & Katchalsky, A. (1971). Network thermodynamics. Nature, 234, 393–399. doi: 10.1038/234393a0.CrossRefGoogle Scholar
  29. 29.
    Oster, G. F., Perelson, A. S., & Katchalsky, A. (1973). Network thermodynamics: Dynamic modelling of biophysical systems. Quarterly Reviews of Biophysics, 6(01), 1–134 doi: 10.1017/S0033583500000081.CrossRefGoogle Scholar
  30. 30.
    Palsson, B. (2006). Systems biology: Properties of reconstructed networks. Cambridge: Cambridge University Press. ISBN: 0521859034.CrossRefGoogle Scholar
  31. 31.
    Palsson, B. (2011). Systems biology: Simulation of dynamic network states. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  32. 32.
    Paynter, H. M. (1961). Analysis and design of engineering systems. Cambridge: MIT Press.Google Scholar
  33. 33.
    Paynter, H. M. (1993). Preface. In J. J. Granda & F. E. Cellier (Eds.), Proceedings of the International Conference On Bond Graph Modeling (ICBGM’93). Simulation Series, La Jolla, CA, USA, January 1993 (Vol. 25). Society for Computer Simulation. ISBN: 1-56555-019-6.Google Scholar
  34. 34.
    Perelson, A. S. (1975). Bond graph junction structures. Journal of Dynamic Systems, Measurement, and Control, 97, 189–195. ISSN: 0022-0434. doi: 10.1115/1.3426901.
  35. 35.
    Polettini, M., & Esposito, M. (2014). Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws. The Journal of Chemical Physics, 141(2), 024117 doi: 10.1063/1.4886396.
  36. 36.
    Qian, H., & Beard, D. A. (2005). Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. Biophysical Chemistry, 114(2–3), 213–220. ISSN: 0301-4622. doi: 10.1016/j.bpc.2004.12.001.
  37. 37.
    Rosenberg, R. C., & Andry, A. N. (1979). Solvability of bond graph junction structures with loops. IEEE Transactions on Circuits and Systems, 26(2), 130–137. ISSN: 0098-4094. doi: 10.1109/TCS.1979.1084615.
  38. 38.
    Sueur, C., & Dauphin-Tanguy, G. (1989). Structural controllability/observability of linear systems represented by bond graphs. Journal of the Franklin Institute, 326, 869–883.MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Sueur, C., & Dauphin-Tanguy, G. (1991). Bond-graph approach for structural analysis of MIMO linear systems. Journal of the Franklin Institute, 328, 55–70.MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Sueur, C., & Dauphin-Tanguy, G. (1997). Controllability indices for structured systems. Linear Algebra and its Applications, 250, 275–287.MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Thoma, J. U., & Atlan, H. (1977). Network thermodynamics with entropy stripping. Journal of the Franklin Institute, 303(4), 319–328. ISSN: 0016-0032. doi: 10.1016/0016-0032(77)90114-4.
  42. 42.
    Thoma, J. U., & Mocellin, G. (2006). Simulation with entropy thermodynamics: Understanding matter and systems with bondgraphs. Heidelberg: Springer. ISBN: 978-3-540-32798-1.zbMATHGoogle Scholar
  43. 43.
    Van Rysselberghe, P. (1958). Reaction rates and affinities. The Journal of Chemical Physics, 29(3), 640–642. doi: 10.1063/1.1744552.CrossRefGoogle Scholar
  44. 44.
    Wellstead, P. E. (1979). Introduction to physical system modelling. Academic Press: New York.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Systems Biology LaboratoryMelbourne School of Engineering, University of MelbourneMelbourneAustralia

Personalised recommendations